Consider the following ODE: p(D)x = f, where p(r) is the degree 2 polynomial p(r) = d Let f(t) = et. We will assume that b, c, s are all real numbers. dt p2 + br +c and D (a) Give non-zero values for b, c and s such that xp(t) = f(t) for all t e R, where xp(t) is a particular solution of the ODE p(D)x = f. (b) Give non-zero values for b, c, s, and also give values for u, v, such that x(t) = g(t) for all t E R, where g(t) = est and x(t) is the unique solution of the ODE p(D)x = g with initial conditions = u and x'(0) = %3D %3D æ(0) = v.

Consider the following ODE: p(D)x = f, where p(r) is the degree 2 polynomial p(r) = d Let f(t) = et. We will assume that b, c, s are all real numbers. dt p2 + br +c and D (a) Give non-zero values for b, c and s such that xp(t) = f(t) for all t e R, where xp(t) is a particular solution of the ODE p(D)x = f. (b) Give non-zero values for b, c, s, and also give values for u, v, such that x(t) = g(t) for all t E R, where g(t) = est and x(t) is the unique solution of the ODE p(D)x = g with initial conditions = u and x'(0) = %3D %3D æ(0) = v.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.4: Zeros Of A Polynomial

Problem 31E

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